Pragmatic trellis coded modulation (PTCM) has become popular because it allows a common basic encoder and decoder to achieve respectable coding gains for a wide range of bandwidth efficiencies (e.g. 1-6 b/s/Hz) and a wide range of coding applications, such as 8-PSK, 16-PSK, 16-QAM, 32-QAM, etc.
In general, PTCM employs primary and secondary modulation schemes. The words "primary" and "secondary" do not indicate relative importance. Rather, the secondary modulation is simply applied to a first subset of information bits, and the primary modulation is applied to the remaining information bits. Conventionally, the secondary modulation scheme differentially encodes its subset of information bits, then encodes these differentially encoded bits with a strong error detection and correction code, such as the well known K=7, rate 1/2 "Viterbi" convolutional code (i.e. Viterbi encoding). The primary modulation scheme need do no more than differentially encode its subset of the information bits. The resulting symbols from the primary and secondary modulation schemes are then concurrently phase mapped to generate quadrature components of a transmit signal. The symbol data are conveyed through the phase and amplitude relationships between the quadrature components of the transmit signal.
Carrier-coherent receiving schemes are often used with PTCM because they demonstrate improved performance over differentially coherent receiving schemes. Coherent receivers become phase synchronized to the received signal carrier in order to extract the amplitude and phase relationships indicated by the quadrature components. However, an ambiguity results because the receiver inherently has no knowledge of an absolute phase reference, such as zero. In other words, where one of 2.sup.K possible phase states are conveyed during each unit interval (i.e. reciprocal of baud), where K equals the number of symbols conveyed per unit interval, then the receiver may identify any of the 2.sup.K phase states as the zero phase state. This ambiguity must be resolved before the conveyed phase and amplitude data successfully reveal the information bits.
Conventionally, the differential encoding allows decoding circuits to eliminate the phase ambiguity problem with respect to the secondary modulation. However, differential encoding and decoding of secondary modulation does not establish an absolute phase reference or solve the ambiguity problem with respect to the primary modulation. When the secondary modulation is decoded, these decoded bits are then used, perhaps with an inverted polarity, to re-generate the secondary modulation for use in decoding the primary modulation.
Unfortunately, such schemes have conventionally been rotationally variant for higher orders of modulation (i.e. higher than QPSK). In other words, at higher orders of modulation the decoders cannot remain locked regardless of which phase reference point is originally selected. As a result, when the decoder locks at some phase states, the differential decoding on the secondary modulation allows the decoder to quickly begin decoding data. However, when the decoder locks at other phase states, an extensive and time consuming normalization rate detection process is performed to regain lock.
The difficulty in achieving rotational invariance is believed to be caused, at least in part, by choosing a scheme for mapping symbols generated by convolutional encoders to phase points which excessively comingles primary and secondary modulation symbols in the resulting phase constellation. For example, conventional digital communication schemes attempt to convey more than one convolutionally encoded symbol from a given secondary information bit stream per unit interval. In addition, conventional digital communication schemes use Gray codes for mapping symbols generated by encoders to phase points. While Gray codes may be desirable for some error detection purposes, they impose an interdependence between adjacent codes (i.e. sequential numbers are represented by expressions that differ by only one bit) that further commingles primary and secondary modulation symbols in the resulting phase constellation.